Wave analysis and control of multiple coupled damped mass-spring systems for two-dimensional waves

Abstract

This paper considers wave analysis and control of two-dimensionally connected damped mass-spring systems. Considering two-dimensional field waves such as longitudinal vibration of plates and out-of-plane motion of membranes, mass motion in the longitudinal direction is considered. The system can be viewed as cascade connected layers composed of vertically connected elements. The system dynamics can be expressed by a recurrence formula. The eigenvalues of the coefficient matrix determine the propagation constants, and the eigenvector elements determine the characteristic admittances. It can be shown that the characteristic polynomial can be decomposed into second order polynomials, which reveals the properties of the propagation constants required for the wave analysis. It can also be shown that the characteristic admittance (impedance matching controller) is a positive real function, which guarantees the closed loop stability. A numerical example illustrates effectiveness of the impedance matching controller for vibration control.